Question

In the following figure, if AB ǁ CD, then find the measure of PCD and CPD.​

Answer 1

Answer:

$CPD = 80$

$PCD = 44$

Explanation:

Given

$AB || CD$

$BAD = 56$

$CPA = 100$

See attachment

Required

Determine PCD and CPD

First, we need to calculate CPD

Since DPA is a straight line and CPA = 100;

We have that:

$CPA + CPD = 180$ --- angle on a straight theorem

Substitute 100 for CPA

$100 + CPD = 180$

Subtract 100 from both sides

$100-100 + CPD = 180-100$

$CPD = 80$

Next, we calculate PCD

We have that:

$DAB= ADC = 56$  --alternate angle

In triangle PCD

$PCD + CPD + PDC = 180$ --- angles in a triangle

Where

$PDC = ADC = 56$

So, we have:

$PCD +80 + 56 = 180$

$PCD +136 = 180$

Subtract 136 from both sides

$PCD = 180 - 136$

$PCD = 44$